We present a joint theoretical and experimental analysis of thermo-refractive noise in high quality factor ($Q$), small mode volume ($V$) optical microcavities. Analogous to well-studied stability limits imposed by Brownian motion in macroscopic Fabry-Perot resonators, we show that microcavity thermo-refractive noise gives rise to a mode volume-dependent maximum effective quality factor. State-of-the-art fabricated microcavities are found to be within one order of magnitude of this bound. By measuring the first thermodynamically-limited frequency noise spectra of wavelength scale high-$Q/V$ silicon photonic crystal cavities, we confirm the assumptions of our theory, demonstrate a broadband sub-$\mu$K/$\sqrt{\mathrm{\text{Hz}}}$ temperature sensitivity, and unveil a new technique for discerning sub-wavelength changes in microcavity mode volumes. To illustrate the immediate implications of these results, we show that thermo-refractive noise limits the optimal performance of recently-proposed room temperature, all-optical qubits using cavity-enhanced bulk material nonlinearities. Looking forward, we propose and analyze coherent thermo-optic noise cancellation as one potential avenue towards violating these bounds, thereby enabling continued development in quantum optical measurement, precision sensing, and low-noise integrated photonics.

中文翻译：

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光学微腔的基本热噪声限制

我们提出了高品质因数热折射噪声的理论和实验联合分析（$问$），小模式音量（$V$）光学微腔。类似于宏观法布里-珀罗谐振器中布朗运动所施加的经过充分研究的稳定性极限，我们表明，微腔热折射噪声会引起与模式体积有关的最大有效品质因数。发现最先进的微腔位于该边界的一个数量级之内。通过测量波长范围高的第一个热力学限制的频率噪声频谱，$问/V$ 硅光子晶体腔，我们证实了我们的理论假设，证明了宽带亚$\mu$K /$\sqrt{\mathrm{\text{赫兹}}}$温度敏感度，并揭示了一种新的技术来识别微腔模式体积中的亚波长变化。为了说明这些结果的直接含义，我们证明了使用腔增强的块状材料非线性，热折射噪声限制了最近提出的室温全光量子比特的最佳性能。展望未来，我们提出并分析相干热光噪声消除技术，作为消除这些界限的一种潜在途径，从而使量子光学测量，精密传感和低噪声集成光子学得以不断发展。